In massive biometric identification systems, response times mainly depends on the database searching algorithms. Thus, in large databases, an increment in the simultaneous queries traffic becomes a critical factor. This paper proposes an algorithm based on the use of a graphic processing unit to solve the exhaustive similarity search for the mass identification of finger veins, using the binary pattern descriptor of the local vertical line and the Hamming distance. The proposed approach reduces the computation time of the searching process over high query traffic by solving each query with a different processing block. The proposed method allows the identification of individuals in a database of 1 million elements, which is the largest database used for finger-vein identification. Experimental results show that our proposed method resolves up to 28 queries simultaneously (over a database of one million individuals) within a time lower than 3 seconds and achieving a speed-up of 283x. To our knowledge, our work is the first implementation of finger-vein recognition on a general-purpose graphics processing unit, which is the main contribution of this document.